Practice Paper

Mahobe

Question One

• Tayla and Naomi travel separately from Mathemahoe to Graftown. Graftown is 240km from Graftown. The graph below shows their distances from Graftown in kilometres, D, and the time, t, in hours.

What is Naomi’s average speed?

40 km/hr

Naomi has been travelling for 4 hours. How far is each girl from Graftown?

Naomi – 80km, Tayla – 60km

Describe Tayla’s journey in relation to Naomi’s journey.

Tayla leaves 1 hour after Naomi and travels at a speed of 60km/hr. She arrives 1 hour before Naomi. After 3 hours they are

both 120 km from Graftown.

Leezah cycles from Newmarket to Graftown. The distance, D, from Graftown is given by

Draw a line on the graph to show Leezah’s distance from Graftown.

Draw a line on the graph to show Leezah’s distance from Graftown.

How long does it take for Leezah to reach Graftown?

4 hours

Tayla’s journey is shown on the graph. Her journey is made up of 2 parts. Write the

equations of both parts.

Question Two

• Use the grids to draw the graphs of

Question Three

• Write the equation of the line drawn.

Question Four

• Bio-fuel made from recycled cooking oil is currently produced for $2.60 per litre. Scientists predict that as their knowledge and technology improves, the cost of production will initially increase but will then decrease until the cost reaches $0.50 per litre. The model for the production cost of 1 litre of bio-fuel from recycled cooking oil over the next 7 years has the formula

The graph of the model is sketched below.C is the production cost per litre and t the time in years.

Using the model, calculate how many years it will take for production cost to start decreasing

2 years because the parabola is moved +2

How long does the model suggest it would take for production costs to be less than $1 per litre?

How long does the model suggest it would take for production costs to be less than $1 per litre?

How long does the model suggest it would take for production costs to be less than $1 per litre?

Question 5

• A hybrid car is fueled by a combination of battery and petrol power.

• It is predicted that the number of taxis that are not hybrid will decrease for the next 4 years at which point all taxis will be hybrid.

In a survey this year no taxis were hybrid. The parabola illustrates this situation. Write the equation of the parabola.

In a survey this year no taxis were hybrid. The parabola illustrates this situation. Write the equation of the parabola.

When t = 4, P = 0.

Use the equation to calculate when 80% of taxis are hybrid.

Use the equation to calculate when 80% of taxis are hybrid. This means 20% are not hybrid.